In a 2018 class activity, 54 students measured how much time (sec) it took to melt each of the following in their mouths: 

(1) A butterscotch chip, 

(2) A chocolate chip, 

(3) A white chip (yes, white is a chip flavor). Each student rolled a die to determine the order in which to melt the chips.
a. Why was it important to randomize the chip order?
b. Besides not having to recruit as many students to get the same number of observations, what is the advantage of using blocking here, versus randomly assigning one chip to each student?

c. Summary quantities include x̅₁ = 88.15, x̅₂ = 60,49, x̅₃ = 72.35, SS(Subject) = 135,833, and SSE = 31,506. Construct an ANOVA table and test at significance level .01 to see whether mean melting time varies by chip flavor.
d. Judging from the F ratio for subjects, do you think that blocking on subjects was effective in this experiment? Explain.